Two black holes spiral around each other not in a smooth dance, but like two stones thrown from opposite banks into a deep whirlpool. Their orbit resembles a highly flattened oval — the eccentricity is nearly one. When they finally collide, a powerful burst of gravitational waves is born — a shudder of space itself. Astronomers catch this 'sound' of a dying pair with giant detectors, but decoding it is tricky: standard models only describe neat, nearly circular approaches.

The authors took 233 computer simulations from the RIT catalog: each one models the merger of two non-spinning black holes of different masses on stretched orbits. From these data, they extracted the dominant tone of the post-merger 'ring'—the so-called (2,2) mode, and built a simple algebraic formula for it. It depends on just three numbers: the mass ratio of the holes and two parameters measured at the moment of merger — the energy and angular momentum of the system. The result is like a tuner's work: instead of running a heavy simulation every time, you can plug numbers into a ready-made expression and immediately hear how the finale sounded.

Such a formula can be directly 'glued' to models describing the approach of the holes before the collision. Then you get a complete picture: from the first orbit to the last fading echo. Astronomers need this not out of idle curiosity. A precise signal template allows them to extract from detector noise the mass, distance, and other properties of the source, and also to check whether the actual spacetime curvature deviates from Einstein's predictions. Eccentric mergers are rare guests, but it is precisely in such extreme conditions that nature may show its hidden cards.